适于图像解压的离散余弦逆变换快速算法

A Fast IDCT Algorithm for Image Decompression

讨论了离散余弦变换(DCT)的基本图像的特性以及实际图像数据的特点,提出了利用基本图像进行二维8×8离散余弦逆变换(IDCT)的快速算法.新算法通过三个技术降低二维8×8IDCT的运算量(1)利用基本图像的对称性;(2)把反量化过程和IDCT融为一步;(3)利用实际图像数据的特点绝大多数量化后的变换系数为零值且非零系数中又有许多的值为±1.理论分析表明,三种技术的融合可大大减少计算量.以多幅标准图像为样本数据,对新方法和当前最有影响的Feig算法做了比较,结果表明文中算法的乘法次数降了约60%,加法次数降了约15%.

The specialities of the basic images of the discrete cosine transform （DCT） and the characteristics of the data of the practical images are discussed, and a fast algorithm for computing 8 × 8 two-dimensional IDCT is presented in this paper. The new algorithm reduces the arithmetic operations by three techniques. The first one is to use the symmetry of the basic images; the second is to combine two steps of computing inverse quantization and IDCT into one, and the last one is to utilize the characteristics of the data of the practical images that the values of the most quantized DCT coefficients of the images are zero, and the values of quite a few of the nonzero quantized DCT coefficients are±1. The theoretic analysis shows that the arithmetic operations are reduced considerably by the combination of the three techniques. By using standard images, the new algorithm is compared with Feig＇s algorithm that is the most influential one nowadays. The results indicate that the new algorithm decreases about 60 percent of multiplying operations and about 15 percent of addition operations.